Finite Group DatabasebetaFinite Group Databasebeta| order | 1020 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D51 |
| unambiguous semidirect product | (C2×C3)⋊(C5×D17) |
| unambiguous semidirect product | (C2×C17)⋊(C5×D3) |
| Fitting, socle | C2×C3×C5×C17 ⋊ C2 |
| derived, Hall | C3×C17 ⋊ C22×C5 |
| Hall | C3×C5×C17 ⋊ C22 |
| Hall | C5×C17 ⋊ C2×D3 |
| Sylow | C17 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ C2×D17 |
| Sylow | C3 ⋊ C2×C5×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C17 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 510 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×D153, C5×D3×D51, C2×C5×C3⋊D51, … |
| maximal normal subgroup of | C2×C3×C5×D51, C2×C5×C11×D51, C2×C5×C13×D51, … |
| maximal quotient of | C2×C5×D153, C5×D3×D51, C2×C5×C3⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1020, 34);